Talk vs. medication. Clinical psychologist might help you through the life-style changes on emotional, cognitive and behavioral levels through various techniques. While psychiatrist are potentially trained in provision of psychotherapy, their primary focus is medication management if the stress becomes unbearable and functioning of the client is impaired.
Psych. Depends on orientation & training, both can do psychotherapy. Psychiatrist can prescribe medications, psychologists perform psychological testing.
Some overlap. Clinical psychologists are trained specifically in a wide range of treatment and assessment methods related to mental illness and other psychological stressors. Psychiatrists are medical doctors who receive specialized training in the treatment of mental illness with medications. Their training may include psychotherapy, but they generally come from a medical-model of treatment.
Therapy vs meds. Speaking very generally, most psychologists hold either a PhD or a PsyD degree (I hold both) and practice psychotherapy. Psychiatrists hold either an MD or a DO degree, and they prescribe psychotropic medications, and generally do not do all that much therapy these days, but years ago psychiatrists would do both.